NOT gate response in a mesoscopic ring: An exact result

We explore NOT gate response in a mesoscopic ring threaded by a magnetic flux $\phi$. The ring is attached symmetrically to two semi-infinite one-dimensional metallic electrodes and a gate voltage, viz, $V_a$, is applied in one arm of the ring which is treated as the input of the NOT gate. The calculations are based on the tight-binding model and the Green's function method, which numerically compute the conductance-energy and current-voltage characteristics as functions of the ring-to-electrodes coupling strength, magnetic flux and gate voltage. Our theoretical study shows that, for $\phi=\phi_0/2$ ($\phi_0=ch/e$, the elementary flux-quantum) a high output current (1) (in the logical sense) appears if the input to the gate is low (0), while a low output current (0) appears when the input to the gate is high (1). It clearly exhibits the NOT gate behavior and this aspect may be utilized in designing an electronic logic gate.